Spaces of D-paraanalytic elements
D. Przeworska-Rolewicz
GDML_Books, (1990), p.

Let X be a linear space. Consider a linear equation(*) P(D)x = y, where y ∈ E ⊂ X,with a right invertible operator D ∈ L(X) and, in general, operator coefficients. The main purpose of this paper is to characterize those subspaces E ⊂ X for which all solutions of (*) belong to E (provided that they exist). This leads, even in the classical case of ordinary differential equations with scalar coefficients, to a new class of C∞-functions, which properly contains the classes of analytic functions of a real variable and of functions vanishing together with all derivatives at a point.

CONTENTSIntroduction..............................................................................51. Preliminaries........................................................................52. Spaces of smooth elements.................................................83. Spaces of D-analytic elements...........................................214. Spaces of D-paraanalytic elements....................................325. Characterization of .D-paraanalytic elements by means of property (c) and canonical mappings.............396. D-R paraanalytic functions .................................................477. Smooth elements in Leibniz D-algebras..............................598. Weak E-solutions................................................................639. Linear systems with scalar coefficients...............................7910. Linear boundary value problems .....................................82References.............................................................................97

1985 Mathematics Subject Classification: 47B99, 47E05, 26E20

EUDML-ID : urn:eudml:doc:268585 
@book{bwmeta1.element.zamlynska-5a511669-2f9c-4539-8b66-fda9c0b6b613,
     author = {D. Przeworska-Rolewicz},
     title = {Spaces of D-paraanalytic elements},
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1990},
     zbl = {0727.47034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-5a511669-2f9c-4539-8b66-fda9c0b6b613}
}

D. Przeworska-Rolewicz. Spaces of D-paraanalytic elements. GDML_Books (1990),  http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-5a511669-2f9c-4539-8b66-fda9c0b6b613/